64 lines
2.2 KiB
Matlab
64 lines
2.2 KiB
Matlab
function [ldens,Dldens,D2ldens] = lpdfig2(x,s,nu)
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% Evaluates the logged INVERSE-GAMMA-2 PDF at x.
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%
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% X ~ IG2(s,nu) if X = inv(Z) where Z ~ G(nu/2,2/s) (Gamma distribution)
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%
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% See L. Bauwens, M. Lubrano and J-F. Richard [1999, appendix A] for more details.
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%
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%
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% INPUTS
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% x [double] m*n matrix of locations,
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% s [double] m*n matrix or scalar, First INVERSE-GAMMA-2 distribution parameters,
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% nu [double] m*n matrix or scalar, Second INVERSE-GAMMA-2 distribution parameters.
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%
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% OUTPUTS
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% ldens [double] m*n matrix of logged INVERSE-GAMMA-2 densities evaluated at x.
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% Dldens [double] m*n matrix of first derivatives of logged INVERSE-GAMMA-2 densities.
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% D2ldens [double] m*n matrix of second derivatives of logged matrix of logged INVERSE-GAMMA-2 densities.
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%
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% SPECIAL REQUIREMENTS
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% none
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% Copyright © 2004-2021 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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ldens = -Inf( size(x) ) ;
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idx = find( x>0 ) ;
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if length(s)==1
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ldens(idx) = -gammaln(.5*nu) - (.5*nu)*(log(2)-log(s)) - .5*(nu+2)*log(x(idx)) -.5*s./x(idx);
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else
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ldens(idx) = -gammaln(.5*nu(idx)) - (.5*nu(idx)).*(log(2)-log(s(idx))) - .5*(nu(idx)+2).*log(x(idx)) -.5*s(idx)./x(idx);
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end
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if nargout >1
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Dldens = ldens;
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if length(s)==1
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Dldens(idx) = - .5*(nu+2)./(x(idx)) + .5*s./x(idx).^2;
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else
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Dldens(idx) = - .5*(nu(idx)+2)./(x(idx)) + .5*s(idx)./x(idx).^2;
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end
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end
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if nargout == 3
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D2ldens = ldens;
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if length(s)==1
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D2ldens(idx) = .5*(nu+2)./(x(idx)).^2 - s./x(idx).^3;
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else
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D2ldens(idx) = .5*(nu(idx)+2)./(x(idx)).^2 - s(idx)./x(idx).^3;
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end
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end |